Of course, you should never sell the car to the dealer and should always make the effort to sell private party, which will often get you 50% or more greater than the dealers best offer.
Yes there are all those arguments. But it's a lot more work for still a pitiful amount of money.
Then on top of that after COVID dealer gave me $5k tradein for an Ecoboost car with a leaking cylinder wall, check engine light, missing parts, etc. where KBB was less than that. I really don't get it.
50% is a stretch. 20% maybe, depending on the vehicle.
But here is another consideration. Sales tax. If I buy a car and trade one in, the sale price that I pay taxes on is the price of the vehicle I am buying minus the trade in.
For instance, if I buy a new car for $30,000 and trade in a vehicle and they give me $15k for it, I pay sales tax only on $15k. That saves me about $1k in my area in sales tax. If I could have sold the used car for over $16k, then I would technically be money ahead. But your time is also worth something. For it to be worth it to me, I would need to be able to get at least $17k for the used vehicle to make it worth the effort.